Impulsive Control Strategy for a Nonautonomous Food-Chain System with Multiple Delays

Abstract

A nonautonomous food-chain system with Holling II functional response is studied, in which multiple delays of digestion are also considered. By applying techniques in differential inequalities, comparison theorem in ordinary differential equations, impulsive differential equations, and functional differential equations, some effective control strategies are obtained for the permanence of the system. Furthermore, effects of some important coefficients and delays on the permanence of the system are intuitively and clearly shown by series of numerical examples. − 3 ( ) ( ) ( ) 3 ( ) + ( ) , = ( ) ( 2 ( ) 2 ( ) ( − 5 ) 2 ( ) + ( − 5 ) + 3 ( ) 3 ( ) ( − 6 ) 3 ( ) + ( − 6 ) − ( ) ( − 3 )) , ̸ = , ( + ) = (1 + 1 ) ( ) , Hindawi Publishing Corporation